STOCKHOLM BRAIN INSTITUTE
KTH Campus
Perceptual and memory functions
in a cortex-inspired attractor
network model
Anders Lansner
Dept of Computational Biology
KTH and Stockholm University
Donald Hebb’s brain
theory
STOCKHOLM BRAIN INSTITUTE
Hebb D O, 1949: The Organization of Behavior
Bliss and Lömo, 1973
Levy and Steward, 1978
LTP/LTD, STDP, ...
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Cell assembly = mental object
Gestalt perception
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Perceptual completion
Perceptual rivalry
• Milner P: Lateral inhibition
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After activity  500 ms
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Figure-background segmentation
Persistent, sustained
Fatigue = Adaptation, synaptic depression
Generalizes to associative memory
• Association chains
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Time-asymmetric synaptic W
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Mathematical instanciations of
Hebb’s theory
STOCKHOLM BRAIN INSTITUTE
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1960’s-70’s Willshaw, Palm, Anderson, Kohonen
e.g. Hopfield network 1982
Recurrently connected
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Layer 2/3, hippocampal CA3, olfactory cortex
Sparse connectivity and activity
• Human cortical connectivity (10-6)
• Activity (<1%)
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Modular
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Kanter, I. (1988). "Potts-glass models of neural
networks." Physical Rev A 37(7): 2739-2742
Extensively studied
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Simulations, e.g. memory properties
Theoretical analysis
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Efficient content-addressable memory!
CNS Stockholm July 25 2011
Question, outline of talk
STOCKHOLM BRAIN INSTITUTE
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Can such an recurrent associative “attractor” memory be
implemented by a network of real neurons and synapses?
• If so, what relation to cortical functional architecture and what
emergent dynamics?
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Top-down approach, complements data driven
First simulations early 1980’s
First journal publication Lansner and Fransén Network: Comput
Neural Syst 1992
TALK OUTLINE
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Model network description
Simulation of basic perceptual and memory function
Spike discharge patterns and population oscillations
Simulation of some basic ”cognitive” functions
CNS Stockholm July 25 2011
From conceptual and abstract
models to biophysics
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Computational units?
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Neuron
Minicolumn
Distributed sub-network
Species differences?
Repetitive functional modules?
• Hyper/Macrocolumns
• How general?
Hubel and Wiesel
icecube V1 model
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Peters and Sethares
1997
Yoshimura and
Callaway 2005
A layer 2/3 cortex model
Microcircuit layout “Icecube - Potts” like
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70% -1.5 mV
70% 1.2 mV
70% 2.5 mV
25% 2.4 mV
117%
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30 pyramidal cells, connected 25%
2 dendritic targeting, vertically projecting inhibitory interneurons
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RSNP, e.g. Double bouquet
Hypercolumns (soft WTA modules) with
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0.30 mV
Minicolumns/local sub-networks with
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230%
2.5 mV
Pool of Basket cells
Martinotti cells, with facilitating synapses from pyramidal cells
Large models: 100 minicolumns, 200 basket + Martinotti cells per hypercolumn
Currently rudimentary layers 4 and 5
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The layer 2/3 cortex model
Single cell model
STOCKHOLM BRAIN INSTITUTE
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Hodgkin-Huxley formalism
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Na, K, KCa, Ca-channels
CaAP and CaNMDA pools
Pyramidal cells
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6 compartments
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Inhibitory interneurons
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3 compartments
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IS, soma, dendritic
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AP and AHP shapes
Firing properties, adaptation
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Neuron populations
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Cell size spread (±10%)
Large-scale networks
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CNS Stockholm July 25 2011
IS, soma, 1 basal, 3 apikal dendritic
SPLIT simulator (by KTH)
Parallel NEURON
NEST simulator
The layer 2/3 cortex model
Synaptic properties and connectivity
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Synaptic transmission
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Local
RSNP
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Distant
pyramidal
Synaptic targeting of soma and dendrites
3D geometry  delays
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Glutamate (AMPA & voltage dependent NMDA)
Depressing synapses
GABAA
0.1 - 1m/s conduction speed
Realistic amplitude of PSP:s in larger network models
Local
basket cell
pre
Local
pyramidal
post
Pyramidal-pyramidal fast synaptic depression
[Tsodyks, Uziel, Markram 2000]
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Conceptual model of Neocortex
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Hypercolumns
Cortical areas
• Hypercolumns are grouped into cortical areas of
various sizes
• Human V1 has ~40000 hypercolumns
• Human neocortex has about 110 cortical areas
(Kaas, 1987)
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Network layout
STOCKHOLM BRAIN INSTITUTE
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One of the 9
hypercolumns
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1x1 mm patch
9 hypercolumns
Each hypercolumn
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Active
minicolumn
(30 pyramidal
cells)
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Active basket
cell
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Active RSNP
cells
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CNS Stockholm July 25 2011
100 minicolumns
100 basket cells
29700 neurons
15 million synapses
100 patterns stored
W trained offline
(A-)symmetric
9 hypercolumns
Spontaneous activity
STOCKHOLM BRAIN INSTITUTE
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1x1 mm patch
9 hypercolumns
Each hypercolumn
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29700 neurons
15 million synapses
100 patterns stored
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Non-symmetric W
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CNS Stockholm July 25 2011
100 minicolumns
100 basket cells
100 hypercolumns
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Spontaneous activity
• 330000 neurons
• 161 million
synapses
 4x4 mm
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8 rack BG/L simulation
October 2006
STOCKHOLM BRAIN INSTITUTE
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Djurfeldt M, Lundqvist M, Johansson C, Rehn M, Ekeberg Ö, and Lansner A (2008): Brain-scale
simulation of the neocortex on the Blue Gene/L supercomputer. IBM J R&D 52:31-41
22x22 mm cortical patch
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22 million cells, 11 billion synapses
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SPLIT simulator
8K nodes, co-processor mode
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used 360 MB memory/node
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Setup time = 6927 s
Simulation time = 1 s in 5942 s
Massive amounts of output data
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77 % estimated speedup (8K)
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Linear speedup to 4K nodes
Point-point communication slows (?)
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STOCKHOLM BRAIN INSTITUTE
Supercomputing for brain
modeling
100 ops/synapse/ms
Brain simulation
parallellizes very well!
Neuromorphic
HW ...
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100 B/synapse
Feb 2011 on JUGENE
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12
10
Exa
log(Giga)
8
• IBM Blue Gene/P
CNS workshop
• 294912on
cores
Supercomputational
Neuroscience – Tools and
• Spiking cortex model
Applications
N > 30 M
Thursday• 09:00
6 Peta
4
Tera
2
• C > 300 G (Hebbian)
GF
Sign up on
billboard!
• Real
time encoding and
GB
retreival
0
1980
1990
2000
2010
2020
2030
year
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STOCKHOLM BRAIN INSTITUTE
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2000+ neurons
250000+ synapses
5 s = 600 s on PC
Interplay of
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Recurrent excitation
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Cellular adaptation
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Synaptic depression
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(Synaptic facilitation)
Lundqvist M, Rehn M, Djurfeldt M and Lansner A (2006). Attractor
dynamics in a modular network model of the neocortex. Network:
Computation in Neural Systems: 17, 253-276
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Adding an interneuron with
facilitating synapses
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Krishnamurthy, Silberberg, and Lansner 2011, submitted
Silberberg and
Markram Neuron
2007
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Bistability, raster plot formats
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only pyramidal cells
Plot formats
• Raw
• Grouped
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Bistable
• Ground state
• Many active
(coding) states
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Oscillatory
Criticality?
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seconds
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Spontaneous attractor ”hopping”
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Synthetic LFP
Frequency (Hz)
60
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3
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Time (seconds)
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Memory replay at theta
• Fuentemilla et al. Curr Biol 2010
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Stimulus during spontaneous
attractor hopping
Without stimulus
With stimulus
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1.5
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2.5
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Time (seconds)
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3.5
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4.5
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Random long-range W?
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Trained W
Permuted W
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4.5
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5.5
Time (seconds)
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6.5
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7.5
Cortical pairwise connection statistics obeyed in both cases
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Stimulus during ground state +
pattern completion
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Synthetic LFP
Frequency (Hz)
60
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30
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L2/3
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High input sensitivity
From groundstate to
spontaneous wandering
by excitation!
L4
0.4
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0.5
2
0.6
0.7
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0.8
seconds
4
seconds
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0.9
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1.1
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1.2
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Stimulus during ground state
Modulated for persistent activity
STOCKHOLM BRAIN INSTITUTE
Synthetic LFP
Frequency (Hz)
60
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40
30
20
10
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0.5
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1.5
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Time (seconds)
2.5
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3.5
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Attractor rivalry
STOCKHOLM BRAIN INSTITUTE
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seconds
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Hebb’s theory - summary
STOCKHOLM BRAIN INSTITUTE
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Can be implemented with biophysically detailed
neurons and synapses
Basic perceptual and memory functions
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Trained W
Perceptual completion and rivalry
Stimulus sensitivity
Psychophysical reaction/processing times, 100 ms
Theta, beta, and gamma power in LFP
• But .... How many attractors can be stored? On-line STDP ...?
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... and what about emergent dynamical properties,
discharge patterns, oscillations?
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Bistable, irregular low-rate firing,
spike synchronization
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Lundqvist, Compte, Lansner PLOS Comp Biol 2010
Ground state
Active (memory) state
Balanced excitation-inhibition
High CV in both states, >1 during ”hopping”
1Hz/10Hz
Foreground neurons
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Spiking activity
in ground and active state
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Ground state – diffuse
Active state – focused
Vm is oscillatory
• Foreground neurons lead
• Race condition, Fries et al. TINS 2007
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Same number of spikes in ground and
active states
Backgound spikes
Foregound spikes
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Oscillatory spontaneous activity
STOCKHOLM BRAIN INSTITUTE
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CNS Stockholm July 25 2011
Rasterplot from 10000 pyramidal
cells of the network.
Spontaneous switching between
different memory states and a
non-coding ground-state attractor
Alpha-Beta activity corresponds
to the periods of ground state
Theta, lower alpha and gamma
peaks corresponds with active
recall
Theta – gamma phase locking
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Theta-gamma phase locking
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e.g. Sirota et al. Neuron 2008
Attractor
shift
Theta+gamma – memory
retrieval
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Jacobs and Kahana J Neurosci 2009
• Spatial patterns of gamma oscillations
code for distinct visual objects
(intracranial EEG), Fig 6C
-p
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p
2p
Bistability of oscillatory activity
STOCKHOLM BRAIN INSTITUTE
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Our attractor memory model shows stable
population oscillations in both ground and active
state and
Characteristics of in vivo cortical spiking activity
• ... low rate irregular spiking of neurons
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Why is this model more stable than previous ones?
• RSNP inhibitory interneuron?
• Large number of neurons?
• Modularity - hypercolumns and minicolumns?
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Importance of modularity
STOCKHOLM BRAIN INSTITUTE
Hypercolumn
Basket
cells
Minicolumn
Pyramids
RSNPs
Gamma
phaselocking/coherence
Average
Vm of a minicolumn
+ own and external spikes
No modules  high
Modules  0.2-0.3
NMDA less important for stability
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Is attentional blink a by-product
of cortical attractors
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RSVP of e.g. Letters
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Silverstein, D. and A. Lansner Front Comput Neurosci 2011
Two target letters. T1 & T2
T2 missed if too close
After-activity 300-500
ms, suppressing
perception of T2?
Spiking H-H attractor
network model
Attractors stored for
each item
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T1, T2 depolarized
Distractors hyperpolarized
±1 mV
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Attentional blink results
Simulation
STOCKHOLM BRAIN INSTITUTE
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Powerful attentional modulation of
target patterns by ± 1 mV
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Experiment
Lacking ”lag-1 sparing”
Benzodiazepine modulates GABA
(amplitude & time constant)
Boucard et al. 2000, Psychopharmacology 152: 249-255
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Oscillations and WM load
STOCKHOLM BRAIN INSTITUTE
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Synaptic working
memory
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q
Sandberg et al. 2003
Mongillo et al. Science 2008
Stored patterns (LTP) + fast
plasticity
Synaptic augmentation
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Lundqvist, Herman, Lansner 2011 J Cogn Neurosci
a-b
Wang et al. 2006
Presynaptic, non-Hebbian
Storing 1 – 5 memories
Increasing memory load
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Decreased alpha & beta
Increased theta & gamma
Intracranial EEG
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Meltzer et al. Cereb Cortex 2008
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Conclusions
STOCKHOLM BRAIN INSTITUTE
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A Hebbian type associative memory can be built from real cortical neurons and
synapses
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Many extensions and details remain to be investigated
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Cortex-like modular structure, realistic sparse activity and connectivity
Connects some basic perceptual and memory phenomena to underlying neuronal and
synaptic processes
Macroscopic dynamics, neuronal activity similar to that seen in data
Complete the layers and understand their roles
Develop network-of-network architecturs with feed-forward, lateral, feed-back projections
Match new data on long-range connectivity
Temporal dimension, sequential association, serial order
Supercomputers enable brain-scale network models
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Full size brain simulations feasible
Substantial work on scalable simulators and analysis tools remains
Will enable a better understanding of normal and diseased brain function
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Acknowledgements
STOCKHOLM BRAIN INSTITUTE
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Early modeling studies, simulator development
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Later model development and analysis
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EC/IP6/FET/FACETS
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Mikael Lundqvist, PhD student
David Silverstein, PhD student
Pradeep Krishamurthy, PhD student
Data analysis
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EC/IP7/FET/NEUROCHEM
Erik Fransén
Per Hammarlund, Örjan Ekeberg
Mikael Djurfeldt
Pawel Herman, postdoc
STOCKHOLM BRAIN INSTITUTE
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Swedish Foundation for Strategic Research
Swedish Research Council and VINNOVA
IBM
AstraZeneca
Select-And-Act
CNS Stockholm July 25 2011
STOCKHOLM BRAIN INSTITUTE
Thanks for your
attention!
CNS Stockholm July 25 2011